In heterogeneous SIR and SEIR models, the condition for herd immunity is finiteness of the mean recovery time E[1/γ], not the mean recovery rate E[γ].
Final size and convergence rate for an epidemic in heterogeneous populations
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The impact of recovery rate heterogeneity in achieving herd immunity
In heterogeneous SIR and SEIR models, the condition for herd immunity is finiteness of the mean recovery time E[1/γ], not the mean recovery rate E[γ].